The main verb of the sentence is bet, which is a bit hard to recognize since the main clause of the sentence lacks an overt subject for the verb, as almost every other declarative sentence in English will contain, especially in writing. In this case, the understood subject of bet is "I," hence a more formal version of the entire sentence would be
I bet you could do it if your life depended on it or even more formal still, I bet
that you could do it if your life depended on it.
Under this analysis of the entire sentence, both you could do it and
your life depended on it would thus be subordinate or dependent clauses, i.e., each contains a main verb in its own clause but that verb is not the verb of the main or
independent clause which contains the subordinate/dependent clause. Another way to envision the overall structure of the sentence is
I bet X if Y where X is the direct object of bet and
if Y is a conditional clause, a type of subordinate/independent clause, that expresses a circumstance that must be true for the main clause,
I bet X, also to be true. The main verb of your conditional clause is
depended, but again since the whole clause if your life depended on it is "subordinate" to the main clause
(I) bet you could do it, depended cannot be the main verb of the entire sentence.
And if we say that the dependent/subordinate clause (that) you could do it
as a whole functions as the direct object of the main clause verb bet, then neither the auxiliary verb of this clause,
could, nor its main verb, do, can be the main verb of the entire sentence.